SOLUTION: What is the domain of the function f(x) = sqrt(5 - 8x + x^2)?

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Question 1209600: What is the domain of the function f(x) = sqrt(5 - 8x + x^2)?
Answer by mccravyedwin(408) About Me  (Show Source):
You can put this solution on YOUR website!
%22f%28x%29%22+=+sqrt%285+-+8x+%2B+x%5E2%29

The graph of f(x) is in red below.

Let's look at the related graph in green, g(x), which
equals what's under the square root radical:

%22g%28x%29%22+=+5+-+8x+%2B+x%5E2



As we see, f(x) stops when it gets to the leftmost x-intercept of g(x)
and begins again at the rightmost x-intercept of of g(x).

The domain of f(x) INCLUDES both x-intercepts of g(x)

So we find the two x-intercepts of 

%22g%28x%29%22+=+5+-+8x+%2B+x%5E2

which doesn't factor (which shows that the problem-maker is stupid) 

So we stop and turn our attention away from what we're doing while we go 
over to the quadratic formula and solve it, and hope we can remember what 
we were doing before the stupid problem-maker made us stop and do that.

5+-+8x+%2B+x%5E2=0

x%5E2+-+8x+%2B+5=0

x+=+%28-%28-8%29+%2B-+sqrt%28+%288%29%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29+

x+=+%288+%2B-+sqrt%2864-20+%29%29%2F2+

x+=+%288+%2B-+sqrt%2844+%29%29%2F2+

x+=+%288+%2B-+sqrt%284%2A11+%29%29%2F2+

x+=+%288+%2B-+2sqrt%2811+%29%29%2F2+

x+=+%282%284+%2B-+sqrt%2811%29%29%29%2F2+

x+=+4+%2B-+sqrt%2811+%29

So the domain of f(x) is



We use " ] " and " [ " to show that the domain INCLUDES those values. 

Edwin